In this context, delegated powers are the same thing as enumerated powers. These are the powers that are specifically and explicitly granted to the Congress. These powers are listed in Article I, Section 8 of the Constitution.
It is important to distinguish between these delegated or enumerated powers on the one hand and implied powers on the other. The implied powers are powers that the Constitution does not clearly and explicitly give to Congress. Instead, Congress has been allowed to exercise these powers because the Constitution implies (but does not state) that Congress may do so.